Mole and Avogadro’s Number

Mole and Avogadro’s Number:

Mole- For counting ordinary objects we generally use the terms like dozen (= 12) or score (= 20). However, the number of atoms or molecules in a small amount of matter is extremely large. For expressing such huge numbers in a convenient way we require a suitable term. With this aim, the term mole has been defined.

A mole is defined as a collection of as many entities as there are atoms in exactly 12g (or 0.012 kg) of carbon-12.

There are 6.02 x 10²³ atoms in 12 g carbon-12, therefore, a mole is a collection of 6.02 x 10²³ objects. Thus

While expressing the amount of a substance in terms of mole, the nature of entities must be specified. For example, the statement that the amount of substance is one mole of hydrogen does not convey any meaning. We should either say one mole of hydrogen atoms (then the substance would contain 6.02 x 10²³ atoms) or one mole of hydrogen molecules (then the substance would contain 6.02 x 10²³ molecules). Summarizing

One mole of atoms of a particular substance is the amount of substance that contains 6.02 x 10²³ atoms. Similarly, one mole of molecules of a particular substance is the amount of substance that contains 6.02 x 10²³ molecules.

Avogadro’s Number- The number of atoms in 12 g (or 0.012 kg) of carbon-12 is called Avogadro’s number. It is denoted by N_A. Its value has been determined by several methods and its most accepted value is 6.02 x 10²³ per 12 g (or 0.012 kg) of C¹². Now since this number is exactly that number which we have termed as a mole, we can make the following statement:

A mole of atoms (or molecules) of a particular substance contains N_A atoms (or molecules) of that kind.

It is evident from the above definition that the molar mass M can be written as

Taking the case of C¹², it can be seen that N_Am_u equals 0.001 kg/mol. Introducing this value in the above relation

From the above analysis, we find that a mole expressed in grams is numerically equal to the molecular mass M_r. However, it must be noted carefully that whereas M_r is a dimensionless quantity. M has a dimension and is measured in kg/mole (or g/mole).